This paper presents a new model for understanding the appearance of objects that exhibit both body and surface reflection under realistic illumination. Specifically, the model represents the appearance of surfaces that interact with a dominant illuminant and a non-negligible ambient illuminant that may have different spectral power distributions. Real illumination environments usually have an ambient illuminant, and the current dynamic range of consumer cameras is sufficient to capture significant information in shadows. The bi-illuminant dichromatic reflection model explains numerous empirical findings in the literature and has implications for commonly used chromaticity spaces that claim to be illumination invariant but are not in many natural situations. One outcome of the model is the first 2-D chromaticity space for an RGB image that is robust to illumination change given dominant and ambient illuminants with different spectral power distributions.